The longitudinal static stability of an aerodynamically alleviated marine vehicle, a mathematical model

An assessment of the relative speeds and payload capacities of airborne and waterborne vehicles highlights a gap that can be usefully filled by a new vehicle concept, utilizing both hydrodynamic and aerodynamic forces. A high-speed marine vehicle equipped with aerodynamic surfaces is one such concept. In 1904, Bryan & Williams (Bryan & Williams 1904 Proc. R. Soc. Lond. 73, 100-116 (doi:10.1098/rspl.1904.0017)) published an article on the longitudinal dynamics of aerial gliders, and this approach remains the foundation of all the mathematical models studying the dynamics of airborne vehicles. In 1932, Perring & Glauert (Perring & Glauert 1932 Reports and Memoranda no. 1493) presented a mathematical approach to study the dynamics of seaplanes experiencing the planing effect. From this work, planing theory has developed. The authors propose a unified mathematical model to study the longitudinal stability of a high-speed planing marine vehicle with aerodynamic surfaces. A kinematics framework is developed. Then, taking into account the aerodynamic, hydrostatic and hydrodynamic forces, the full equations of motion, using a small perturbation assumption, are derived and solved specifically for this concept. This technique reveals a new static stability criterion that can be used to characterize the longitudinal stability of high-speed planing vehicles with aerodynamic surfaces.